Scalable Statistical Methods for Cell Type Deconvolution and Mixed Models Applied to High Dimensional Genomic Data

Utilizing genomic data in the clinical setting provides new opportunities for biomarker discovery, disease characterization, and personalizing treatment, but also poses new statistical challenges. In the first part of the dissertation, we propose a new computational method, IsoDeconvMM, which estimates cell type fractions using isoform-level RNA-seq gene expression data one gene at a time. The cell type composition of a tissue sample may itself be of interest and is needed for proper analysis of differential gene expression of heterogeneous tissues. Although a variety of existing computational methods estimate cell type proportions using gene-level expression data, isoform-level expression could be equally or more informative for determining cell type origin. In genomics datasets as well as many other modern biomedical datasets, the data are increasingly high dimensional and exhibit complex correlation structures. Generalized linear mixed models (GLMMs) have long been employed to account for such dependencies. In the second part of this dissertation, we implement several statistical and computational innovations to improve the speed of a high dimensional penalized GLMM framework for simultaneously selecting fixed and random effects, resulting in the efficient R package glmmPen. Although this framework extends the feasible dimensionality of GLMMs relative to existing methods, new methodology is needed to alleviate computational burden as the dimension increases and allow scalability to hundreds of predictors. We present a novel reformulation of the GLMM using a factor model decomposition of the random effects, enabling scalable computation of GLMMs in higher dimensions by reducing the latent space from a large number of random effects to a smaller set of common factors. We extend our prior work to estimate model parameters and perform simultaneous selection of fixed and random effects using a modified version of the Monte Carlo Expectation Conditional Minimization (MCECM) algorithm. We show that through this factor model decomposition, we can improve the speed and scalability of fitting high dimensional penalized GLMMs. Finally, we extend our framework on performing high dimensional penalized generalized linear mixed models to survival outcome data. We approximate proportional hazards mixed effects models using piecewise constant hazards mixed effects survival models.Doctor of Philosoph